In parallelogram ABCD, diagonal BD is perpendicular to side AD, angle B is 135 degrees.

In parallelogram ABCD, diagonal BD is perpendicular to side AD, angle B is 135 degrees. The parallelogram area is 49cm2. Find AD

<ADB = <DBC = 90 ° (criss-crossing angles when cutting parallel straight lines).

<ABD = 135 ° – <DBC = 135 ° – 90 ° = 45 °.

<BAD = 180 ° – <ABD – <ADB = 180 ° – 45 ° – 90 ° = 45 °.

If <BAD = <ABD, then triangle ABD is isosceles and AD = BD (1).

The area of the parallelogram is equal to the product of the base AD by the height BD:

S = AD * BD

Taking into account equality (1), the area S can be written in the form:

AD ^ 2 = 49 cm2;

AD = √ (49 cm2) = 7 cm.

Answer: Side AD = 7 cm.